In this paper, an efficient numerical algorithm to find exact solutions for the system of linear equations based on Homotopic Perturbation Method (HPM) is presented. A reliable modification is proposed and the modified method is employed to solve the system of linear equations generated from some models of electrical networks; the results are compared with those obtained by the conventional methods of solving the system of linear equations. Two examples are given to illustrate the ability and reliability of the improved homotopic perturbation method. The results reveal that the improved method is very simple and effective.